networkx.algorithms.community.lukes.lukes_partitioning

lukes_partitioning(G, max_size: int, node_weight=None, edge_weight=None) list[source]

Optimal partitioning of a weighted tree using the Lukes algorithm.

This algorithm partitions a connected, acyclic graph featuring integer node weights and float edge weights. The resulting clusters are such that the total weight of the nodes in each cluster does not exceed max_size and that the weight of the edges that are cut by the partition is minimum. The algorithm is based on LUKES[1].

Parameters
Ggraph
max_sizeint

Maximum weight a partition can have in terms of sum of node_weight for all nodes in the partition

edge_weightkey

Edge data key to use as weight. If None, the weights are all set to one.

node_weightkey

Node data key to use as weight. If None, the weights are all set to one. The data must be int.

Returns
partitionlist

A list of sets of nodes representing the clusters of the partition.

Raises
NotATree

If G is not a tree.

TypeError

If any of the values of node_weight is not int.

References